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RedHat 9 (Linux i386) - man page for cggglm (redhat section l)

CGGGLM(l)					)					CGGGLM(l)

NAME
       CGGGLM - solve a general Gauss-Markov linear model (GLM) problem

SYNOPSIS
       SUBROUTINE CGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO )

	   INTEGER	  INFO, LDA, LDB, LWORK, M, N, P

	   COMPLEX	  A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ), Y( * )

PURPOSE
       CGGGLM solves a general Gauss-Markov linear model (GLM) problem:
	       minimize || y ||_2   subject to	 d = A*x + B*y
		   x

       where  A  is  an  N-by-M  matrix,  B is an N-by-P matrix, and d is a given N-vector. It is
       assumed that M <= N <= M+P, and

		  rank(A) = M	 and	rank( A B ) = N.

       Under these assumptions, the constrained equation is always consistent,	and  there  is	a
       unique  solution  x and a minimal 2-norm solution y, which is obtained using a generalized
       QR factorization of A and B.

       In particular, if matrix B is square nonsingular, then the problem GLM  is  equivalent  to
       the following weighted linear least squares problem

		    minimize || inv(B)*(d-A*x) ||_2
			x

       where inv(B) denotes the inverse of B.

ARGUMENTS
       N       (input) INTEGER
	       The number of rows of the matrices A and B.  N >= 0.

       M       (input) INTEGER
	       The number of columns of the matrix A.  0 <= M <= N.

       P       (input) INTEGER
	       The number of columns of the matrix B.  P >= N-M.

       A       (input/output) COMPLEX array, dimension (LDA,M)
	       On entry, the N-by-M matrix A.  On exit, A is destroyed.

       LDA     (input) INTEGER
	       The leading dimension of the array A. LDA >= max(1,N).

       B       (input/output) COMPLEX array, dimension (LDB,P)
	       On entry, the N-by-P matrix B.  On exit, B is destroyed.

       LDB     (input) INTEGER
	       The leading dimension of the array B. LDB >= max(1,N).

       D       (input/output) COMPLEX array, dimension (N)
	       On entry, D is the left hand side of the GLM equation.  On exit, D is destroyed.

       X       (output) COMPLEX array, dimension (M)
	       Y	(output)  COMPLEX array, dimension (P) On exit, X and Y are the solutions
	       of the GLM problem.

       WORK    (workspace/output) COMPLEX array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK. LWORK >= max(1,N+M+P).	For optimum  performance,
	       LWORK >= M+min(N,P)+max(N,P)*NB, where NB is an upper bound for the optimal block-
	       sizes for CGEQRF, CGERQF, CUNMQR and CUNMRQ.

	       If LWORK = -1, then a workspace query is assumed; the routine only calculates  the
	       optimal	size of the WORK array, returns this value as the first entry of the WORK
	       array, and no error message related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.

LAPACK version 3.0			   15 June 2000 				CGGGLM(l)


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